Related papers: Continuum Free-Energy Computing
The theory of dynamical quantum phase transitions represents an attempt to extend the concept of phase transitions to the far from equilibrium regime. While there are many formal analogies to conventional transitions, it is a major question…
The increasing scale and nonlinearity of modern energy and power system problems pose significant challenges to classical numerical solvers. In parallel, advances in quantum and quantum-inspired hardware are expected to improve scalability…
We introduce a framework designed to analyze the thermodynamics of an abstractly defined logical computer like a deterministic finite automaton (DFA) or a Turing machine, without specifying any extraneous parameters (like rate matrices,…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
The computation of dynamical response functions is central to many problems in condensed matter physics. Owing to the rapid growth of quantum correlations following a quench, classical methods face significant challenges even if an…
We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which enhances the safety properties of programs, but also supports…
The paper assesses stationary probability distributions in out of equilibrium systems. In the phenomenology proposed, no free energy can be well defined. Fluctuations of Landau free energy couplings arise when the intrinsic chemical…
We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
The classical phase-field modeling approaches for multiphase problems represent each phase using a regularized characteristic function, which necessarily introduces a simplex constraint for the phase-field variables. Additionally, the…
In this chapter, we discuss recent advances and new opportunities through methods of machine learning for the field of classical density functional theory, dealing with the equilibrium properties of thermal nano- and micro-particle systems…
Using Molecular Dynamics simulations based on the effective hamiltonian developed by Zhong, Vanderbilt and Rabe [Phys. Rev. Lett. {\bf 73}, 1861 (1994)] (and fitted on first-principles calculations only), the technique of the thermodynamic…
The pursuit of energy transition necessitates the coordination of several technologies, including more efficient and cost-effective distributed energy resources (DERs), smart grids, carbon capture, utilization, and storage (CCUS),…
Our computers today, from sophisticated servers to small smartphones, operate based on the same computing model, which requires running a sequence of discrete instructions, specified as an algorithm. This sequential computing paradigm has…
Orbitally ordered states exhibit unique features which make them a promising platform for exploring the ultrafast dynamics of long-range order in solids: Their free energy typically has multiple discrete minima, and electric laser fields or…
The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on…
We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable…
A standard objective in computer experiments is to approximate the behaviour of an unknown function on a compact domain from a few evaluations inside the domain. When little is known about the function, space-filling design is advisable:…
We study the Landau model for uniaxial incommensurate-commensurate systems of the I class by keeping Umklapp terms of third and fourth order in the expansion of the free energy. It applies to systems in which the soft mode minimum lies…